Who controls the controller? A dynamical model of corruption

ABSTRACT

The aim of this article is to give at least a partial answer to the question made in the title. Several works analyze the evolution of the corruption in different societies. Most of such papers show the necessity of several controls displayed by a central authority to deter the expansion of the corruption. However there is not much literature that addresses the issue of who controls the controller. This article aims to approach an answer to this question. Indeed, as it is well known, in democratic societies an important role should be played by citizens. We show that politically active citizens can prevent the spread of corruption. More precisely, we introduce a game between government and officials where both can choose between a corrupt or honest behavior. Citizens have a political influence that results in the prospects of a corrupt and a non-corrupt government be re-elected or not. This results in an index of intolerance to corruption. We build an evolutionary version of the game by means of the replicator dynamics and we analyze and fully characterize the possible trajectories of the system according to the index of intolerance to corruption and other relevant quantities of the model.

KEYWORDS:

• Corruption
• game theory
• evolutionary theory
• dynamical stability

Notes

¹ Different ways of defining corruption and its limitations are considered in (Jain, 2001).

² The vote buying consists in the bribery of a group of citizens with the aim of obtaining their vote in favor of the re-election. The voter would be compensated with cash or some bonus. This modus operandi is well documented in literature, see for instance (Grego, 2013) and (Allen & Allen, 1981).

³ It should be noted that in most circumstances, a dictatorial regime also has elections that are fraudulent (for example, pre-1974 Portugal). Thus, our model may also explain these situations.

⁴ We assume that costs associated with the capture of a corrupt official are funded by sanctions that a non-corrupt government obtains from fines to corrupt officials. Certainly if this cost exceeds the total amount of fines collected, the government will have to appeal to other sources to perform this task. This point is not considered in this work.

⁵ Most indexes measuring corruption actually measure proxies for corruption because corruption is a difficult phenomenon to measure. An example of such an empirical index of the perceived governmental corruption is Transparent International’s (TI) Corruption Perceptions Index (CPI). This index captures information about administrative and political aspects of corruption. However, its use has not come without criticism (see (Campbell, 2013)).

⁶ Recent events in South Korea, where citizens unanimously reacted to the corrupt practices of Prime Minister Park Geun-hye suggest that, if the Index of Intolerance of citizens to Corruption is high enough, it is possible to exert political pressure that can maybe result in stopping the growth of corruption. See http://www.abc.ne t.au/news/2016-11-15/south-korea-park-geun-hye-hopes-political-crisis-be-contained/8024978.